Artificial potential function guidance (APFG) has been widely and successfully used to solve motion planning problems across a variety of domains. APFG is popular, in large part, due to its simplicity and speed. However, APFG is known to have several limitations. Notably, it may not find a free trajectory even where one exists, and in most cases APFG trajectories are highly suboptimal. In contrast, fueled by the development of new numerical optimization algorithms, there has been considerable recent interest in the use of a variety of optimal trajectory planners which do not exhibit these limitations. These algorithms hinge on finding a trajectory which minimizes a given cost functional. When successful these algorithms find very high-quality trajectories, but when applied to nonlinear systems and cluttered environments, they often run too slowly for use in real-time systems, and providing rigorous convergence guarantees for such algorithms may be difficult. This paper demonstrates an apparently unappreciated relationship between APFG and a form of optimal planning called receding horizon planning. This understanding may be used to derive trajectory planning algorithms which fit into an anytime planning framework, which may allow high-quality trajectories to be calculated with guaranteed real-time performance. Preliminary results for a receding horizon planner applied to planar holonomic robotic navigation problem and to a realistic orbital robotic arm grapple maneuver are presented.
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